Radial Influx Research Articles

Experimental study on the negative pressure loss generated by the gas influx process around a long borehole

In the process of gas extraction in long boreholes, gas influx in the radial direction causes a non-uniform variable mass flow field due to bore wall friction. This flow field can lead to a negative pressure decay along the hole length, thus affecting the gas extraction effect. With this effect in mind, a gas variation mass test was designed for pore-containing specimens with different pore wall roughnesses. It is also based on the variable mass flow pressure drop theory and analyzes the pressure variation, hole wall roughness, and gas influx rate inside the borehole. The result indicates that radial influx of gas along the borehole wall can interfere with the main flow in the borehole. The increase of the radial influx flow rate of the gas produces an obvious swirling phenomenon, which gradually makes the fluid mixing flow situation more and more complicated the more it differs from the mainstream velocity. The mainstream velocity and the pore wall influx velocity are the main factors causing mixing loss. The study results are important for understanding the long borehole gas sink process and the design of reasonable borehole parameters.

Concentric Eyewall Formation in Typhoon Sinlaku (2008). Part III: Horizontal Momentum Budget Analyses

This is a follow-up work to two prior studies examining secondary eyewall formation (SEF) in Typhoon Sinlaku (2008). This study shows that, in the SEF region, the majority of the elevated winds are supergradient. About two-thirds of the rapid increase in tangential wind tendencies immediately prior to SEF are attributed to agradient wind tendencies. This suggests the importance of nonlinear, unbalanced dynamical processes in SEF in addition to the classical axisymmetric balanced response to forcings of heating and momentum. In the SEF region, analyses show two distinct responsible processes for the increasing azimuthal tangential wind in two vertical intervals. Within the boundary inflow layer, the competing effect between the mean radial influx of absolute vorticity and deceleration caused by surface friction and subgrid diffusion yields a secondary maximum of positive tendency. Analyses further demonstrate the major impact of the mean radial influx of absolute vorticity on SEF. Above the boundary inflow layer, the vertical advection acts to vertically extend the tangential wind jet via the lofting of the enhanced tangential momentum farther upward. The roles of the nonlinear unbalanced dynamics in these two processes are discussed in this paper. From a Lagrangian perspective, the persistently increasing agradient force outweighs the frictional loss, effectively decelerating boundary layer inflowing air across the SEF region. This explains the sharpening of the radial gradient of boundary layer inflow, which is shown to be responsible for the buildup of a zone with concentrated boundary layer convergence. The previously proposed unbalanced dynamical pathway to SEF is elaborated upon and supported by the current results and discussion.

The role of heating and cooling associated with ice processes on tropical cyclogenesis and intensification

A recent idealized numerical study of tropical cyclogenesis and subsequent intensification using warm‐rain‐only microphysics is extended to examine the modifications brought about by a representation of ice processes. It is found that the time taken to reach cyclogenesis is more than twice that in the equivalent warm‐rain‐only simulation. The subtle reasons for the difference in the length of the gestation period are discussed. A mid‐level vortex forms during the early gestation period when ice processes are present, but not when warm‐rain‐only processes are present. Axisymmetric balance calculations show that the spin‐up of this mid‐level vortex is related to the different spatial distribution of diabatic heating rate in the presence of ice, which leads to a system‐scale radial influx of absolute vorticity in the middle troposphere. The tropical‐cyclone vortex that forms in the simulation with ice is similar to that in the warm‐rain‐only simulation, with the strengthening frictional boundary layer exerting a progressively important role in focusing inner‐core deep convection. This vortex develops in situ on a much smaller scale than the mid‐level vortex and there is no evidence that it is a result of the mid‐level vortex being somehow carried downwards, as has been suggested previously by some researchers. Some implications of the results in relation to previous theories of tropical cyclogenesis are discussed.

Direct and inverse problems of gas emission and the sorptive deformation of coal beds

Using the equations of state for fractured-porous media that describe the sorptioninduced deformation of coal, we develop a geomechanical model for radial gas influx to a borehole drilled in a coal bed with the concurrent evolution of stress field in the borehole environment. A numerical-and-analytical method is proposed for solving the corresponding system of equations for poroelastic media. A relation is found between the volume of slack withdrawn in the borehole (when opening up the gas-bearing seams), the sorption-and-storage capacities of coal, the permeability k, and the horizontal component σ h of the natural stress field. We demonstrate the solvability of the inverse boundary-coefficient problem of determining k and σ h on the basis of pressure in the closed borehole. We substantiate an express-method for estimating the permeability by the measurements of pressure in the borehole operating in the “pressure drop” mode.

Stabilization of vortex beams in Kerr media by nonlinear absorption

We elaborate a new solution for the problem of stable propagation of transversely localized vortex beams in homogeneous optical media with self-focusing Kerr nonlinearity. Stationary nonlinear Bessel-vortex states are stabilized against azimuthal breakup and collapse by multiphoton absorption, while the respective power loss is offset by the radial influx of the power from an intrinsic reservoir. A linear stability analysis and direct numerical simulations reveal a region of stability of these vortices. Beams with multiple vorticities have their stability regions too. These beams can then form robust tubular filaments in transparent dielectrics as common as air, water and optical glasses at sufficiently high intensities. We also show that the tubular, rotating and speckle-like filamentation regimes, previously observed in experiments with axicon-generated Bessel beams, can be explained as manifestations of the stability or instability of a specific nonlinear Bessel-vortex state, which is fully identified.

Sensitivity of Axisymmetric Tropical Cyclone Spinup Time to Dry Air Aloft

AbstractThe sensitivity of tropical cyclone spinup time to the initial entropy deficit of the troposphere is examined in an axisymmetric hurricane model. Larger initial entropy deficits correspond to less moisture above the initial lifting condensation level of a subcloud-layer parcel. The spinup time is quantified in terms of thresholds of integrated horizontal kinetic energy within a radius of 300 km and below a height of 1.5 km. The spinup time increases sublinearly with increasing entropy deficit, indicating the greatest sensitivity lies with initial moisture profiles closer to saturation. As the moisture profile approaches saturation, there is a large increase in the low-level, area-averaged, vertical mass flux over the spinup period because of the predominance of deep convection. Higher entropy deficit experiments have a greater amount of cumulus congestus and reduced vertical mass flux over a longer duration. Consequently, the secondary circulation takes longer to build upward, and the radial influx of angular momentum is reduced. There is also a reduction in the conversion of potential available enthalpy to horizontal kinetic energy, as a result of reduced flow down the radial pressure gradient early in the spinup period. Later in the spinup period, the low-level vortex spins up relatively quickly near the nascent radius of maximum wind in the high-entropy deficit experiments, whereas the low-level vortex spins up over a wider area in the low-entropy deficit experiments.

On the secondary eyewall formation of Hurricane Edouard (2014).

A first observationally-based estimation of departures from gradient wind balance during secondary eyewall formation is presented. The study is based on the Atlantic Hurricane Edouard (2014). This storm was observed during the National Aeronautics and Space Administration's (NASA) Hurricane and Severe Storm Sentinel (HS3) experiment, a field campaign conducted in collaboration with the National Oceanic and Atmospheric Administration (NOAA). A total of 135 dropsondes are analyzed in two separate time periods: one named the secondary eyewall formation period and the other one referred to as the decaying-double eyewalled storm period. During the secondary eyewall formation period, a time when the storm was observed to have only one eyewall, the diagnosed agradient force has a secondary maxima that coincides with the radial location of the secondary eyewall observed in the second period of study. The maximum spin up tendency of the radial influx of absolute vertical vorticity is within the boundary layer in the region of the eyewall of the storm and the spin up tendency structure elongates radially outward into the secondary region of supergradient wind, where the secondary wind maxima is observed in the second period of study. An analysis of the boundary-layer averaged vertical structure of equivalent potential temperature reveals a conditionally unstable environment in the secondary eyewall formation region. These findings support the hypothesis that deep convective activity in this region contributed to spin up of the boundary layer tangential winds and the formation of a secondary eyewall that is observed during the decaying-double eyewalled storm period.

Influence of Radial Flux Inflow Profile on Pressure Drop of Perforated Horizontal Wellbore

In this study, the authors have attempted to present five different profiles for a uniform radial influx through a perforated wellbore. The total pressure drop is not only frictional, accelerational and gravitational pressure drops, but also by the inflow pressure drop that is caused by the inflow through the perforation. The inflow through the wellbore model affects the shear stress due to the wall friction. The influence of inflow depends on the flow regime present in the wellbore. Numerical simulations were performed using ansys fluent 14-cfx, where the governing equations of mass and momentum were solved simultaneously, using the two equations of a standard k–ε turbulence model. The results proved that the behavior of wall shear stress followed the shape of the radial inflow, i.e., the shear stress increased with the increase of radial flow and decreased with the decrease of radial flow. It was found that the fluid influx has increased the apparent friction factor along the horizontal wellbore, but in some cases the influx is decreased.

The Pressure Drop Model of Liquid Flow with Wall Mass Transfer in Horizontal Wellbore with Perforated Completion

The fluids in horizontal wells can exhibit complicated flow behaviors with wall mass transfer, partly due to the interaction between the main flow and the radial influx along the wellbore and the completion parameters used. This paper presents a novel regression model established based on the experiment data retrieved from the available literatures to determine the apparent friction factor for a single phase wellbore flow. The proposed model has the potential to be readily applicable to different perforation parameters, such as shot phasing and shot density. Compared with other models in the same practical example which is offered by Ouyang et al., the model of this paper to calculate the wellbore pressure is applicable and reasonable. This new model can be easily incorporated into reservoir simulators or analytical reservoir and horizontal wellbore inflow coupling models.

The Pretornadic Phase of the Goshen County, Wyoming, Supercell of 5 June 2009 Intercepted by VORTEX2. Part II: Intensification of Low-Level Rotation

Abstract The dynamical processes responsible for the intensification of low-level rotation prior to tornadogenesis are investigated in the Goshen County, Wyoming, supercell of 5 June 2009 intercepted by the second Verification of the Origins of Rotation in Tornadoes Experiment (VORTEX2). The circulation of material circuits that converge upon the low-level mesocyclone is principally acquired along the southern periphery of the forward-flank precipitation region, which is a corridor characterized by a horizontal buoyancy gradient; thus, much of the circulation appears to have been baroclinically generated. The descending reflectivity core (DRC) documented in Part I of this paper has an important modulating influence on the circulation of the material circuits. A circuit that converges upon the low-level mesocyclone center prior to the DRC’s arrival at low levels (approximately the arrival of the 55-dBZ reflectivity isosurface in this case) loses some of its previously acquired circulation during the final few minutes of its approach. In contrast, a circuit that approaches the low-level mesocyclone center after the DRC arrives at low levels does not experience the same adversity. An analysis of the evolution of angular momentum within a circular control disk centered on the low-level mesocyclone reveals that the area-averaged angular momentum in the nearby surroundings of the low-level mesocyclone increases while the mesocyclone is occluding and warm-sector air is being displaced from the near surroundings. The occlusion process reduces the overall negative vertical flux of angular momentum into the control disk and enables the area-averaged angular momentum to continue increasing even though the positive radial influx of angular momentum is decreasing in time.

Clouds in Tropical Cyclones

Abstract Clouds within the inner regions of tropical cyclones are unlike those anywhere else in the atmosphere. Convective clouds contributing to cyclogenesis have rotational and deep intense updrafts but tend to have relatively weak downdrafts. Within the eyes of mature tropical cyclones, stratus clouds top a boundary layer capped by subsidence. An outward-sloping eyewall cloud is controlled by adjustment of the vortex toward gradient-wind balance, which is maintained by a slantwise current transporting boundary layer air upward in a nearly conditionally symmetric neutral state. This balance is intermittently upset by buoyancy arising from high-moist-static-energy air entering the base of the eyewall because of the radial influx of low-level air from the far environment, supergradient wind in the eyewall zone, and/or small-scale intense subvortices. The latter contain strong, erect updrafts. Graupel particles and large raindrops produced in the eyewall fall out relatively quickly while ice splinters left aloft surround the eyewall, and aggregates are advected radially outward and azimuthally up to 1.5 times around the cyclone before melting and falling as stratiform precipitation. Electrification of the eyewall cloud is controlled by its outward-sloping circulation. Outside the eyewall, a quasi-stationary principal rainband contains convective cells with overturning updrafts and two types of downdrafts, including a deep downdraft on the band’s inner edge. Transient secondary rainbands exhibit propagation characteristics of vortex Rossby waves. Rainbands can coalesce into a secondary eyewall separated from the primary eyewall by a moat that takes on the structure of an eye. Distant rainbands, outside the region dominated by vortex dynamics, consist of cumulonimbus clouds similar to non–tropical storm convection.

Clouds in Tropical Cyclones

Clouds within the inner regions of tropical cyclones are unlike those anywhere else in the atmosphere. Convective clouds contributing to cyclogenesis have rotational and deep intense updrafts but tend to have relatively weak downdrafts. Within the eyes of mature tropical cyclones, stratus clouds top a boundary layer capped by subsidence. An outward-sloping eyewall cloud is controlled by adjustment of the vortex toward gradient-wind balance, which is maintained by a slantwise current transporting boundary layer air upward in a nearly conditionally symmetric neutral state. This balance is intermittently upset by buoyancy arising from high-moist-static-energy air entering the base of the eyewall because of the radial influx of low-level air from the far environment, supergradient wind in the eyewall zone, and/or small-scale intense subvortices. The latter contain strong, erect updrafts. Graupel particles and large raindrops produced in the eyewall fall out relatively quickly while ice splinters left aloft surround the eyewall, and aggregates are advected radially outward and azimuthally up to 1.5 times around the cyclone before melting and falling as stratiform precipitation. Electrification of the eyewall cloud is controlled by its outward-sloping circulation. Outside the eyewall, a quasi-stationary principal rainband contains convective cells with overturning updrafts and two types of downdrafts, including a deep downdraft on the band’s inner edge. Transient secondary rainbands exhibit propagation characteristics of vortex Rossby waves. Rainbands can coalesce into a secondary eyewall separated from the primary eyewall by a moat that takes on the structure of an eye. Distant rainbands, outside the region dominated by vortex dynamics, consist of cumulonimbus clouds similar to non–tropical storm convection.

Transient gas-liquid two-phase flow in pipes with radial influx or efflux

Transient gas-liquid two-phase flow in pipes with radial influx or efflux

A novel approach to the in situ measurement of oxygen concentrations in the sapwood of woody plants

AbstractA novel technique for the physico‐chemical analysis of xylem sap by underwater access to the sapwood of trees is described. In situ measurements of dissolved oxygen in the sapwood are performed by combining this technique with a novel optical method for oxygen detection. In early spring, the oxygen concentration of the sapwood of Betula pendula was in the range of 80–230 µmol O2 L−1, corresponding to an oxygen deficit of 40–75% of air saturation. Oxygen concentration maxima and minima occurred early in the morning and in the afternoon, respectively, whereas xylem sap temperatures showed the reverse pattern. In the sapwood, hypoxia increased from the beginning of bud break until frondescence, when a deficit of 86% of air saturation marked the upper limit of oxygen depletion. There seemed to be no relationship between daily variations of oxygen concentration and xylem sap pressure. In summer, sap flow was a major determinant for the diurnal variation of dissolved oxygen concentration. Oxygen supply to the sapwood was determined by both radial influx into the trunk through intercellular gas spaces and transport of dissolved oxygen via xylem sap flow. Radial influx seemed to be favoured during night‐time, when the trunk was warmer than ambient air. During daytime, the hypoxia of the sapwood rose and increased sharply in the evening, when sap flow velocity approximated zero. High temperature in the sapwood enhanced the respiratory oxygen consumption of the wood parenchyma while the supply of dissolved oxygen via the transpiration stream became ineffective.

Transient gas–liquid two-phase flow in pipes with radial influx or efflux

A simplified model for transient gas–liquid flow in pipes with radial influx or efflux has been developed in this paper. The resulting governing equations are essentially hyperbolic with U tp+ c s and U tp− c s as their eigenvalues. A finite-difference scheme based on the split coefficient matrix (SCM) approach is applied to solve the mass and momentum balance equations. Sample numerical simulation runs are performed. Simulation results agree with experimental observations and clearly show the features of variation in pressure drop, liquid holdup, and two-phase velocity during transient and steady state flow periods.

A homogeneous model for gas–liquid flow in horizontal wells

Radial influx or outflux stands for the major difference between fluid flow in a pipe and fluid flow in a well. A homogeneous model for gas–liquid flow in a horizontal well is presented in this paper. In addition to frictional and gravitational components of total pressure drop, accelerational pressure drops due to fluid expansion and radial influx or outflux are considered. Effect of radial influx or outflux on wall friction is also taken account for. With a segmented approach, the new model and several existing pipe flow models have been applied to predict pressure drop along a wellbore, and predictions are compared with experimental data. It is found that the new homogeneous model outperforms existing models for gas–liquid flow in horizontal wells.

Modelling Multi-lateral Wells

Abstract A computation scheme was implemented in a general-purpose, finite-difference simulator to model multi-lateral wells. Frictional pressure drop along the wellbore and proper fluid mixing at lateral connection points were included in the calculation of the wellbore pressure profile for each lateral. The formulation is general and a lateral can be branched out from any point along the main well path. Since the production profile of each lateral is influenced by the wellbore pressure distribution, the prediction accuracy depends on a good wellbore flow model. The Beggs and Brill(1) correlation and the homogeneous flow model were implemented, along with a new model proposed by Ouyang et al.(2) which included an acceleration term and accounted for the lubrication effect due to radial influx. Well performance prediction results using the three models were compared. The impacts of different tubing sizes on the well performance and the production contribution from each lateral were studied. Introduction Recently multi-lateral wells have been employed in off-shore platforms or remote and hard to access terrain areas to save costs comparing with drilling multiple vertical or horizontal wells. This work is to study the pressure and production profiles along each lateral using different pipe flow models. The vertical standoffs of laterals to GOC or WOC, the optimal length of laterals, the angles between laterals, the completion PI values used in simulation, and the optimal number of laterals are other important factors in designing multi-lateral wells. However, these issues will not be addressed here. Numerical Method The completion production rate and wellbore pressure profiles along each lateral are closely related. There is also interaction between laterals. The fluid dynamics calculation inside the wellbore can be described as follows: Pipeflow Calculation There are many steady-state correlations available to calculate frictional pressure losses. In this work, we implemented three models, namely, the Beggs and Brill model, the homogeneous model, and a modified homogeneous model (including radial inflow effect) in a general-purpose reservoir simulator. The homogeneous model gave a better pressure match for the Stanford/Marathon two-phase flow tests(3,4). It was a very simplified model. For two-phase flow, it used a mixing rule to calculate the density and viscosity values of the gas-liquid mixture. Then it used the mixture properties in the single-phase fluid-wall frictional loss formula. We did not use a transient pipeflow model(5) because it would require much longer computing time. Radial Inflow Effect Rigorously speaking, the regular pipe flow calculation is not suitable for open hole or perforation intervals due to the presence of radial inflow from the reservoir. For turbulent flow, the radial inflow provides a so called "lubrication effect" and reduces the frictional loss(6,7). For laminar flow (rarely occurring in oil field practice), it increases the frictional loss(8). Here we used a formula proposed by Ouyang et al.(3) to model radial inflow effect, Equation (1) (Available In Full Paper) where ƒo is the corrected frictional coefficient due to radial inflow and ƒ is the wall friction coefficient. For the open hole, Rew can be expressed as Equation (2) (Available In Full Paper)

The Influence of a Local Swirl Ratio on Tornado Intensification near the Surface

Abstract The results of high-resolution, fully three-dimensional, unsteady simulations of the interaction of a tornado with the surface are presented. The goal is to explore some of the range of structures that should be expected to occur in nature within the tornadic “corner flow”—that region where the central vortex meets the surface. The most important physical variables considered are the tornado-scale circulation and horizontal convergence, the effective surface roughness, the tornado translation speed, the low-level inflow structure, and the upper-core structure. A key ingredient of the corner flow dynamics is the radial influx of fluid in the surface layer with low angular momentum relative to that of the fluid in the main vortex above it. This low swirl fluid arises initially from outside or below the larger-scale vortex or through frictional loss of angular momentum to the surface and forms much of the vortex core flow after it exits the corner flow region. Changes in the surface layer inflow or ...

Particle Entrainment in a Bounded Rotating Flow With a Drain

A bathtub vortex is usually formed at the axis of a drain. In the presence of such a vortex, gravity separation of solid impurities lighter than the embedding fluid is modified by centrifugal separation and viscous resuspension. Both mechanisms are responsible for the agglomeration of impurities at the axis of the vortex. From there the impurities are easily sucked into the outlet. In the investigated case, a viscous fluid with a given initial rotation is spinning down in a container with endplates both at the bottom and the top. The amount of fluid withdrawn through a circular hole in the center of the vortex is constantly replaced by a radial influx. The resulting time-dependent flow was solved by means of a finite difference method taking into account the influence of Ekman layers at the bottom and the top. Subsequently, the process of centrifugal separation of particles lighter than the embedding fluid was studied in the aforementioned flow field. The results were compared with the particle motion in a classical Oseen vortex. For a simplified case an analytical solution was derived and compared with the corresponding numerical solution. Both results were found to be in good agreement.

Pipeline Flow of Gas, Liquid And Sand Mixtures At Low Velocities

Abstract Experiments have been conducted to investigate the ability of gas-liquid mixtures to transport sand in a horizontal pipe or well at low velocities. Both laminar and turbulent liquid flow regimes! were investigated. The gas-containing flows were predominant1y in the slug regime. Sand transport rates in laminar oil flows were very low until the axial pressure gradient exceeded 1.5 kPaim. Gas addition did not improve this performance. With turbulent liquid flows, sand transport rates at low velocities could be estimated by the Meyer-Peter equation as long as the sand particle diameter exceeded 0.1 mm. As the gas flowrate increased, sand transport rates eventually exceeded these predictions because of mixing caused by passage of the slugs. Axial pressure gradients for turbulent gas-liquid-sand mixtures could be estimated from the Lockhart-Martinelli correlation. Introduction Horizontal wells are of growing importance in petroleum production in Western Canada and the flow within these wells have been under investigation at the Saskatchewan Research Council since 1990. Experimental studies have been conducted with the goal of defining the approaches to be taken in mechanistic modelling of wellbore flows of allldnds. Since as many as four phases (oil, water, gas and sand) may be present, a systematic investigation of gradually increasing complexity has been undertaken. In the first investigation, the effects of radial influx at a slotted section of wellbore were examined(1). Axial pressure gradients for single phase flows were shown to be predictable from the known laws of laminar and turbulent flow. No additional complications such as turbulence generation were detected in the experiments. When a stationary sand layer was present, the ability of the influx to mobilize the sand could be explained in terms of concepts defmed by previous studies of liquid-solid fluidization. Thus over a wide range of experimental conditions, a horizontal well with fluid influx resembles a horizontal pipe whose flowrate increases with distance downstream. A second investigation(2) studied the ability of a turbulent (water) flow to transport sand at low velocities above a stationary deposit. A threshold velocity for sand transport was observed and at at velocities just above the threshold, the flow resembled that which occurs in channels with stationary bottom deposits. Very fine particles, 0.01 mm in diameter, were uniformly distributed in the flow by the turbulence. In this case pressure gradients and sand transport rates could be predicted rather easily by treating the sand-liquid mixture as a pseudo-liquid. The transport rates for sands of diameter 0.2 and 0.1 mm could be predicted from the empirical Meyer-Peter equation(3) which is known to describe channel sediment transport. However this equation was completely unsatisfactory for very fine (0.01 mm) particles. At higher velocities, but with a stationary deposit still present, pressure gradients and solids throughputs could be predicted from a three layer model which was derived from the two layer model which is known to describe well the flow of slurries in deposit-free pipelines(4). The transition from the mechanistic layer model regime to the Meyer-Peter regime seemed to occur where dune formation in the stationary layers became predominant.